 # What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5? Lewis Harvey 2021-01-31 Answered
What is the probability of the random occurrence of a value between 56 and 61 from a normally distributed population with mean 62 and standard deviation 4.5?
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Step 1
The normal distribution:
A continuous random variable X is said to follow normal distribution with mean $\mu$ and standard deviation $\sigma$ if the probability density function of X is,
$f\left(x\right)=\frac{1}{\sigma \sqrt{2\pi }}{e}^{\frac{{\left(x-\mu \right)}^{2}}{2{\sigma }^{2}}},-\propto 0$
Step 2
Finding the probability of the random occurrence of a value between 56 and 61:
The random occurrence of a value (X) follows a normal distribution with mean 62 and standard deviation of 4.5.The required probability is calculated as follows:
$P\left(56